Is it possible to state an outliers detection problem as a reinforcement learning problem?
It is quite often possible to frame a problem as a Reinforcement Learning (RL) problem at some level. However, this may turn out to be for no benefit, or a net cost towards solving the problem. Casting parameter or hyperparameter searches as RL can be adding a layer of complexity and reduce efficiency.

One key thing to bear in mind is that any classification or regression that occurs within a RL framework will end up using effectively the same models and approaches that could solve the same problems directly. These models would either appear directly as the function approximators in RL that implement policies or value functions, or they would be an implied part of them. If you have labeled data for classification - even delayed until some time after you collect data, then you are usually going to be better off using supervised learning directly. 

For hyperparameter searches (e.g. cutoffs for anomaly detection) then you may not need labelled data, but just need a good way to test the model offline.

The first point at which supervised learning or classic anomaly detection might fail for you is if you never receive any feedback about individual records, only a measure of overall performance. In other words, if you can measure consequences of good performance, but never measure or check  correctness.

Your characterisation


  about 7-10% of data do not make any sense.


does not appear to fit that. It looks like you could detect this, maybe manually labelling a few thousand records, and train a classifier using supervised learning techniques. That is likely a much better use of your time than trying to restructure the problem at a higher level and trusting a trail-and-error approach to discover the same rules.

Putting that to one side, assuming you do have a problem where


data to be classified is arriving as a stream, and needs to be processed online, item by item or in small batches
you have reason to think that an accept/reject stage before processing further would be useful
you have no way to label training data for accept/reject
you have a way to measure performance of the remaining system after the accept/reject phase


then you could use RL to frame the accept/reject phase as an action. There are some challenges there, but essentially you would use RL along with measurement feedback to sample errors or gradients - typically using TD Error or policy gradients. This could wrap almost any model that does classification or anomaly detection etc, provided it could be trained using those gradients.

From comments, if the underlying distributions for accept/reject are non-stationary, this may point you more towards a RL solution. However, that may come with a cost to performance - you will need to balance exploration rate (which will reduce the performance of the model against stationary data) versus speed of learning new distributions. This is a problem for all online learners; the main advantage of a RL approach here is that it will not require generating new labelled data. If you can use a recency-weighted anomaly detection algorithm instead, then you won't need the labeled data either - whether that is better requires testing, personally I'd take a working anomaly detection as the baseline and only use RL if it proved itself better.

The specific items that you turn into states and rewards are not clear to me from the question, and you would need to work on these things carefully. It is possible you will need more than the current data item in order to define state, and that will depend a lot on how the feedback loop works that establishes reward.